Question

If x = 1 +${{\frac{1}{3}_{+ \frac{1}{2}}}_{+ \frac{1}{3}}}_{+ \frac{1}{2}...........\infty}$ Then value of x is –

• A. $\sqrt{\frac{3}{5}}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\sqrt{\frac{5}{3}}$

Answer 1

Answer: (D)

$\sqrt{\frac{5}{3}}$

Answer 2

x = 1 + $\frac{1}{3 + \frac{1}{1 + x}}$

Ю x = 1 + $\frac{1 + x}{4 + 3x}$ Ю 3x² = 5 Ю x = ± $\sqrt{\frac{5}{3}}$

But x is positive Ю x = $\sqrt{\frac{5}{3}}$